First, assume \(c=1\)  so that the Cluster operation in Algorithm  is moot and \(\lbrace \mathcal {G}_{(j)}\rbrace _{j=1}^c = \mathcal {G}\) .
Recall from Section REF  that the output \(\mathbf {Y}^{(i)}\)  of every sub-GCN has the same dimensions as the output of the global model, thus, each sub-GCN can be trained to minimize the same global loss function considered for the learning problem of interest.
In this way, GIST is flexible by being agnostic to the specific loss function chosen by the practitioner.
Then, one application of subTrain in Algorithm  corresponds to one step of stochastic gradient descent.
This synchronous and independent training of sub-GCNs is inspired by local SGD [1]} and is conducted on separate GPUs, facilitating a parallelized implementation.
